If a spaceship orbits the earth at a height of 500 km from its surface, then determine its (i) kinetic energy, (ii) potential energy, and (iii) total energy (iv) binding energy. Mass of the satellite = 300 kg, Mass of the earth `= 6xx10^(24) kg`, radius of the earth `= 6.4 xx 10^(6) m, G=6.67 xx 10^(-11) "N-m"^(2) kg^(-2)`. Will your answer alter if the earth were to shrink suddenly to half its size ?

Explanation

To solve the problem step by step, we will calculate the kinetic energy, potential energy, total energy, and binding energy of a spaceship orbiting the Earth at a height of 500 km.

### Given Data:
- Mass of the satellite (m) = 300 kg
- Mass of the Earth (M) = \(6 \times 10^{24}\) kg
- Radius of the Earth (R) = \(6.4 \times 10^{6}\) m
- Height of the satellite (h) = 500 km = \(500 \times 10^{3}\) m
- Gravitational constant (G) = \(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\)
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